publication . Preprint . Article . 2018

Mixed global anomalies and boundary conformal field theories

Tokiro Numasawa; Satoshi Yamaguch;
Open Access English
  • Published: 01 Nov 2018
We consider the relation of mixed global gauge gravitational anomalies and boundary conformal field theory in WZW models for simple Lie groups. The discrete symmetries of consideration are the centers of the simple Lie groups. These mixed anomalies prevent to gauge them i.e, take the orbifold by the center. The absence of anomalies impose conditions on the levels of WZW models. Next, we study the conformal boundary conditions for the original theories. We consider the existence of a conformal boundary state invariant under the action of the center. This also gives conditions on the levels of WZW models. By considering the combined action of the center and charge...
arXiv: High Energy Physics::Theory
free text keywords: High Energy Physics - Theory, Condensed Matter - Statistical Mechanics, Condensed Matter - Strongly Correlated Electrons, Anomalies in Field and String Theories, Discrete Symmetries, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798, Nuclear and High Energy Physics, Quantum electrodynamics, Orbifold, Conformal map, Boundary conformal field theory, Boundary value problem, Invariant (mathematics), Wess–Zumino–Witten model, Physics, Lie group, Conformal field theory, Theoretical physics

[1] G. 't Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, NATO [2] C. Csaki and H. Murayama, Discrete anomaly matching, Nucl. Phys. B 515 (1998) 114 [3] X. Chen, Z.-C. Gu, Z.-X. Liu and X.-G. Wen, Symmetry protected topological orders and the group cohomology of their symmetry group, Phys. Rev. B 87 (2013) 155114 [21] N. Bultinck, R. Vanhove, J. Haegeman and F. Verstraete, Global anomaly detection in two-dimensional symmetry-protected topological phases, Phys. Rev. Lett. 120 (2018) 156601 [22] D.S. Freed and C. Vafa, Global anomalies on orbifolds, Commun. Math. Phys. 110 (1987) [23] G. Felder, K. Gawedzki and A. Kupiainen, Spectra of Wess-Zumino-Witten models with arbitrary simple groups, Commun. Math. Phys. 117 (1988) 127.

[24] O.M. Sule, X. Chen and S. Ryu, Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument, Phys. Rev. B 88 (2013) 075125 [arXiv:1305.0700] [25] C. Vafa, Modular Invariance and Discrete Torsion on Orbifolds, Nucl. Phys. B 273 (1986) [27] D. Gepner and E. Witten, String Theory on Group Manifolds, Nucl. Phys. B 278 (1986) 493 [28] P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory, Graduate Texts in Contemporary Physics, Springer-Verlag, New York U.S.A. (1997).

[29] R. Dijkgraaf and E. Witten, Topological Gauge Theories and Group Cohomology, Commun.

[38] A. Roy and T. Quella, Chiral Haldane phases of SU(N ) quantum spin chains, Phys. Rev. B [39] F. Pollmann, A.M. Turner, E. Berg and M. Oshikawa, Entanglement spectrum of a topological phase in one dimension, Phys. Rev. B 81 (2010) 064439.

[40] K. Tanimoto and K. Totsuka, Symmetry-protected topological order in SU(N ) Heisenberg [41] J. Cardy and E. Tonni, Entanglement hamiltonians in two-dimensional conformal eld theory, J. Stat. Mech. 1612 (2016) 123103 [arXiv:1608.01283] [INSPIRE].

[42] V. Alba, P. Calabrese and E. Tonni, Entanglement spectrum degeneracy and the Cardy formula in 1 + 1 dimensional conformal eld theories, J. Phys. A 51 (2018) 024001 [44] S. Singh and G. Vidal, Symmetry protected entanglement renormalization, Phys. Rev. B 88 [45] G. Evenbly and G. Vidal, Algorithms for Entanglement Renormalization: Boundaries, Impurities and Interfaces, J. Stat. Phys. 157 (2014) 931 [arXiv:1312.0303].

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publication . Preprint . Article . 2018

Mixed global anomalies and boundary conformal field theories

Tokiro Numasawa; Satoshi Yamaguch;